Quantum information processing device and method

ABSTRACT

Quantum information processing device includes resonator incorporating material containing physical systems, each of physical systems having at least four energy states, transition between two energy states of at least four energy states, and transition energy between at least two energy states of at least four energy states, at least four energy states being non-degenerate when magnetic field fails to be applied to physical systems, transition resonating in resonator mode that is in common between physical systems, each of at least four energy states representing a quantum bit, transition energy being shifted when magnetic field is applied to physical systems, and magnetic-field application unit configured to apply magnetic field having direction and intensity to material, to eliminate linear transition energy shift between two energy states included in physical systems, each of two energy states included in physical systems being with excluding two energy states resonating in resonator mode.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is based upon and claims the benefit of priority fromprior Japanese Patent Application No. 2005-376497, filed Dec. 27, 2005,the entire contents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a quantum information processing methodinvolving a magnetic-field application method for a physical system, inwhich coherence time is extended by the magnetic field applied to thesystem, to effectively utilize the extended coherence time in a quantuminformation processing device that uses a resonator mode. It alsorelates to a quantum information processing device capable ofeffectively utilizing the coherence time.

2. Description of the Related Art

In quantum information processing devices such as quantum computers,information (quantum bit information) is represented by superposedstates related to a certain physical state of a physical system, such asan atom, ion or photon. In this case, information processing is realizedby iterating, for example, individual operations of quantum bits, orconditional gate operations in which interaction between a pair ofphysical systems is introduced so that a change in a quantum bitcorresponding to one of the physical systems will cause a change in aquantum bit corresponding to the other physical system.

It is necessary for each physical system to hold the coherency of itsphysical quantity during information processing. Accordingly, physicalsystems with a long coherence time are required. Coherence time meansthe time until coherence is lost, and hence is also called de-coherencetime. The coherence time of the hyperfine structure level of rare-earthions dispersed in an oxide crystal is exceptionally long for a solid,and can be controlled using electromagnetic radiation of nearvisible-light frequencies. This being so, rare-earth ions are highlypromising as physical systems that enable a quantum informationprocessing device to be constructed using a solid material (see, forexample, K. Ichimura, K. Yamamoto and N. Gemma, Phys. Rev. A 58(5],4116(1998); and K. Ichimura, Opt. Common. 196, 119(2001)).

Further, a dominant method for extending the coherence time of thehyperfine structure level of crystalline rare-earth ions has recentlybeen proposed (see, for example, E. Fraval, M. J. Sellars, and J. J.Longdell, Phys. Rev. Lett. 92(7), 077601(2004)). It has been confirmedexperimentally that this method can achieve a remarkable increase incoherence time. However, in general, the de-coherence that can beconsiderably suppressed at a time is only that between a pair of energystates.

When using crystalline rare-earth ions in a quantum informationprocessing device, the use of a resonator mode is almost indispensableat present. However, in the case of using the resonator mode, nospecific magnetic-field application methods are known, which clarify,for example, between which energy states de-coherence should besuppressed, or when a magnetic field should be applied, in order toactually utilize the effect of suppression of de-coherence bymagnetic-field application in the quantum information processing device.

BRIEF SUMMARY OF THE INVENTION

In accordance with a first aspect of the invention, there is provided aquantum information processing device comprising: a resonatorincorporating a material containing a plurality of physical systems,each of the physical systems having at least four energy states,transition between two energy states of the at least four energy states,and transition energy between at least two energy states of the at leastfour energy states, the at least four energy states being non-degeneratewhen a magnetic field fails to be applied to the physical systems, thetransition resonating in resonator mode that is in common between thephysical systems, each of the at least four energy states representing aquantum bit, the transition energy being shifted when the magnetic fieldis applied to the physical systems; and a magnetic-field applicationunit configured to apply a magnetic field having a direction and anintensity to the material, to eliminate a linear transition energy shiftbetween two energy states included in the physical systems, each of thetwo energy states included in the physical systems being with excludingthe two energy states resonating in the resonator mode.

In accordance with a second aspect of the invention, there is provided aquantum information processing device comprising: a resonatorincorporating a material containing a plurality of physical systems,each of the physical systems having a plurality of energy states andtransition between two energy states of the plurality of energy states,the transition resonating in the resonator mode that is in commonbetween the physical systems, each of energy states that are degenerateand are included in the plurality of energy states representing aquantum bit; a magnetic-field application unit configured to apply amagnetic field to the physical systems; a light source unit configuredto output a laser beam; a separation unit configured to separate thelaser beam into a plurality of laser beams; a laser control unitconfigured to control phase, intensity and frequency of each of thelaser beams, the laser control unit converting the laser beams intopulse laser beams; an emission unit configured to emit the controlledlaser beams to the physical systems; and a magnetic-field control unitconfigured to control application of the magnetic field, themagnetic-field control unit causing the magnetic-field application unitto interrupt the application of the magnetic field only when adiabaticpassage for a two-qbit (i.e., quantum bit) gate operation is performedbetween two of the physical systems utilizing the resonator mode.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

FIG. 1 is a view illustrating the relationship between a commonresonator mode and a plurality of ion energy states indicating aplurality of quantum bits;

FIG. 2 is a view illustrating the relationship, employed in quantuminformation processing devices and methods according to embodiments,between energy states set to the critical point and a resonator mode,where quantum bits are represented by energy states that are notdegenerated when no magnetic field is applied;

FIG. 3 is a view illustrating the relationship between the time ofapplying a magnetic field, the energy state and the resonator mode,assumed, in the quantum information processing devices and methods ofthe embodiments, where quantum bits are represented by degeneratedenergy states when no magnetic field is applied;

FIG. 4 is a block diagram illustrating part of a quantum informationprocessing device according to a first embodiment, in which energystates are set to the critical point where quantum bits are representedby energy states that are not degenerated when no magnetic field isapplied;

FIG. 5 is a view illustrating the energy states of three Pr³⁺ ionsemployed in the first embodiment;

FIG. 6 is a view illustrating the entire quantum information processingdevice used for performing a gate operation in the first or secondembodiment; and

FIG. 7 is a view illustrating the energy states of two Pr³⁺ ionsemployed in the second embodiment.

DETAILED DESCRIPTION OF THE INVENTION

Quantum information processing devices and methods according toembodiments of the invention will be described in detail with referenceto the accompanying drawings.

In the quantum information processing devices and methods utilizing acommon resonator mode, according to embodiments of the invention, thesignificantly extended coherence time of quantum bits can be actuallyused for quantum information processing.

Firstly, a description will be given of the essential matter of thequantum information processing devices and methods of the embodiments.In the embodiments described below, energy states are set to thecritical point, described later, by applying a magnetic field thereto.The resultant energy states in which the coherence time is significantlyextended are assumed to be those that contain no energy statesresonating in the resonator mode and stores quantum information for along time. The quantum information processing devices and methods of theembodiments effectively utilize the long coherence time acquired by theapplication of the magnetic field, thereby increasing the maximum numberof executable steps (the number of executions of a series of quantumoperations), or the number of such steps and quantum bits. Namely, theembodiments of the invention can increase the processing capacity basedon quantum computation.

Further, in the quantum information processing devices and methods ofthe embodiments, when no external magnetic field is applied and quantuminformation is represented by degenerated energy states, if a constantmagnetic field is continuously applied except during the execution ofthe adiabatic passage method in a two-qbit gate operation that utilizesdegeneration, quantum information processing, in which the maximumnumber of executable steps, or the number of both such steps and quantumbits is increased, can be realized.

Before giving a detailed description of the quantum informationprocessing devices and methods according to the embodiments of theinvention, the mechanism will be described which enables the coherencetime to be extended in a manner effective to quantum informationprocessing, and enables the number of steps, or the number of steps andquantum bits to be significantly increased.

The embodiments of the invention utilize the above-mentioned methodproposed by Fraval et al. (E. Fraval, W. J. Sellars, and J. J. Longdell,Phys. Rev. Lett. 92(7), 077601(2004)) for suppressing, by theapplication of a magnetic field, the de-coherence between the states ofthe nuclear spin of each of rare-earth ions dispersed in a material(e.g., crystal). When the rare-earth ions dispersed in the crystal arecooled down to the temperature of liquid helium, the factor that causesthe states of the nuclear spin of each rare-earth ion to lose coherenceis the fluctuation in the intensity of the magnetic field generated ateach ion, which is caused by fluctuation in the state of the nuclearspin of each atom and ion of the crystal. In the method of Fraval etal., a magnetic field of a direction and intensity unique to certain twoenergy states of the nuclear spin of each of the dispersed rare-earthions is applied to the two energy states, so that a linear shift (firstorder Zeeman shift) in transition energy between the two energy stateswith respect to the magnetic field will disappear or become extremelysmall. In this state, the certain two energy states are represented tobe at the three-dimensional critical point. When such a magnetic fieldas the above is applied, the de-coherence between the two energy statesis suppressed.

Fraval et al. detected that when a magnetic field of (x, y, z)=(732,173, −219)G, which sets, to the critical point, the states m_(I)=+½

+ 3/2 of the nuclear spin of Pr³⁺:Y₂SiO₅ that assumes the electronicground state, the coherence time is extended to 82 ms from a maximumvalue of about 500 μs measured till that time. The C₂-axis of thecrystal is the y-axis, and the polarization direction of the opticaltransition between ³H₄ and ¹D₂ is the z-axis.

At the critical point, the attenuation of a Raman heterodyne spin echosignal indicating de-coherence is represented not by a simpleexponential function but by I=I₀ exp{−(2t/T_(M))²}, and 82 ms indicatinga coherence time corresponds to T_(M) (phase memory time) in theequation. Further, in the equation, I is the intensity of the Ramanheterodyne spin echo signal, I₀ is the initial intensity of the Ramanheterodyne spin echo signal, and t is the time. The factor that causesde-coherence under these conditions is already analyzed, and thecoherence time can be further extended if a pulse stream is applied (E.Fraval, W. J. Sellars, and J. J. Longdell, Phys. Rev. Lett. 95,030506(2005)). They also detected that if a magnetic field of about 30 Gis applied, the coherence time between degenerated energy states isremarkably extended (m_(I)=+ 3/2

− 3/2, 5.86 ms).

Concerning the increase in coherence time by the application of amagnetic field, the following features are acquired:

(1) In general, the de-coherence that can be significantly suppressed bythe setting to the critical point is only that between a pair of energystates which are not degenerated when no magnetic field is applied; and

(2) The coherence time between energy states that are degenerated whenno magnetic field is applied is extended by the application of amagnetic field.

When crystal with rare-earth ions dispersed therein is utilized in aquantum information processing device, it is practical to utilize aresonator mode and interaction between quantum bits, as is symbolicallyshown in FIG. 1. The resonator mode is so-called “invisible wiring”.Since it is difficult to accurately position ions adjacent to each otherto cause them interact with each other, it is simple and reliable toutilize the resonator mode.

The resonator mode is utilized to perform conditional gate operationsbetween two physical systems that provide quantum bits. The physicalsystems are operated so that different energy states in the systemssequentially represent various quantum bits in accordance with variousoperations or states, such as individual operations of quantum bits(using a one-quantum-bit gate), conditional gate operations between twoquantum bits, or no operations for maintaining the energy states as theyare. To perform such operations as the above on each ion, ions that havedifferent transition energies between their energy states are used asquantum bits (FIG. 1 does not show the differences in transitionenergies between ions), and the frequency of light to be applied isadjusted to that of each ion to be operated.

In the examples of FIG. 1, concerning the ions (i.e., 1^(st) to(k−1)^(th), (k+1)^(th) to (l−1)^(th) and (l+1)^(th) to n^(th) ions),which are not yet subjected to a gate operation, quantum bits realizedby them are represented by, for example, |A> and |B>. Further, only forthe ions (k^(th) and l^(th) ions) subjected to a two-qbit gateoperation, |C> is temporarily used to represent quantum bits. However,quantum information is not necessarily shifted to |C> in both the k^(th)and l^(th) ions or simultaneously in both the k^(th) and l^(th) ions.

When information processing using quantum bits is performed as describedabove, it is difficult to simultaneously set, to the critical point, theenergy states of physical systems that represent different quantum bits,for the following reasons:

Firstly, when a quantum information processing device that processesquantum bits is operating, different physical systems assume differentstates that represent different quantum bits, therefore it is necessaryto apply magnetic fields of different directions and intensities inaccordance with the states of the physical systems, which is notpractical.

Secondly, there is a case where two or more quantum bits are representedby a single physical system (e.g., a single ion). In this case, theenergy states representing different quantum bits cannot simultaneouslybe set to the critical point.

In light of the above, it is practical to simultaneously apply amagnetic field of a certain intensity and direction to all physicalsystems. As the two energy states to be set to the critical point by themagnetic field to thereby remarkably extend the coherence time, it iseffective to select the two energy states that can hold quantum bits forthe longest time, i.e., to select the two energy states that canrepresent quantum bits for the longest time during informationprocessing.

As will be described later in the first embodiment of the invention, theenergy states that do not resonate in the resonator mode, e.g., |A> and|B>, can represent quantum bits for a longer time. When a two-qbit gateoperation is required between two target quantum bits in two physicalsystems, the energy states that resonate in the resonator mode are usedonly to represent the target quantum bits, thereby executing thetwo-qbit gate operation based on the resonator mode. The other quantumbits are maintained represented by the energy states that do notresonate in the resonator mode, so as not to be influenced by thetwo-qbit gate operation performed between the above-mentioned quantumbits. After executing the two-qbit gate operation, even the two targetquantum bits subjected to the two-qbit gate operation are returned tothe energy states that do not resonate in the resonator mode.

In the embodiments of the invention, in the case of quantum informationprocessing in which the energy states that are not degenerated when nomagnetic field is applied represent quantum bits (see, for example, H.Goto and K. Ichimura, Phys. Rev. A 70(1), 012305(2004)), two energystates, which need to hold quantum bits for a long time and contain noenergy state that resonate in the resonator mode, are set to thecritical point (corresponding to the above-mentioned feature (1)),thereby enabling the effective use of the remarkably extended coherencetime (FIG. 2).

In the case of quantum information processing in which quantum bits arerepresented by two degenerated energy states, these degenerated energystates cannot be set to the critical point. However, if a magnetic fieldis applied to the degenerated energy states, they are returned tonon-degenerated energy states and hence the coherence time is extended(corresponding to the above-mentioned feature (2)). Accordingly, it isdesirable to continue the application of a magnetic field if the quantumbits need to be held. The intensity of the magnetic field is determinedfrom the type of crystal, and the energy level of degeneration. However,in the known two-qbit gate operation utilizing the resonator mode (see,for example, K. Ichimura, Opt. Column. 196, 119(2001)), it is necessaryto interrupt the application of a magnetic field when the adiabaticpassage method is used between two physical systems that represent twotarget quantum bits. This is because the adiabatic passage methodutilizes degenerated energy states. Accordingly, a magnetic-fieldapplying method is useful, in which a magnetic field is applied in asteady state, and the application of the magnetic field is interruptedonly when using the adiabatic passage method for the two-qbit gateoperation (FIG. 3).

As described above, in the quantum information processing devicesutilizing the resonator mode, according to the embodiments of theinvention, when the coherence time is extended by the application of amagnetic field, the extended coherence time can be effectively utilizedfor quantum information processing if the energy states which should beset to the critical point and the time when the states are set to thecritical point, are appropriately selected.

First Embodiment

Referring to FIG. 4, a description will be given of a quantuminformation processing device and method according to a firstembodiment.

The first embodiment is directed to an example corresponding to theabove-described feature (1) “In general, the de-coherence that can besignificantly suppressed by the setting to the critical point is onlythat between a pair of energy states which are not degenerated when nomagnetic field is applied.”

As shown in FIG. 4, the quantum information processing device of thefirst embodiment comprises a controller 401, rare-earth dispersedcrystal 404, resonator 405, coils 406 to 408, cryostat 409 and rotationunit 410. The controller 401 includes a magnetic-field designation unit402 and rotation-designating unit 403.

The controller 401 controls the direction and intensity of the magneticfield applied to the rare-earth dispersed crystal 404. Themagnetic-field designation unit 402 adjusts the levels of the current tobe supplied to the coils 406 to 408, thereby adjusting the direction andintensity of the resultant magnetic field. The rotation unit 410three-dimensionally rotates the rare-earth dispersed crystal 404.Namely, the rotation unit 410 can rotate the rare-earth dispersedcrystal 404 about each of the three axes that are not parallel to eachother. The rotation unit 410 can control the direction of the magneticfield applied to the rare-earth dispersed crystal 404.

Although FIG. 4 shows the coils 406 to 408 and rotation unit 410, onlythe coils 406 to 408 can control the direction and intensity of themagnetic field applied to the rare-earth dispersed crystal 404. Further,even a combination of the rotation unit 410 and any one of the coils 406to 408 can control the direction and intensity of the magnetic fieldapplied to the rare-earth dispersed crystal 404. The coils 406 to 408are, for example, electromagnets or superconducting magnets.

The rare-earth dispersed crystal 404 is crystal with rare earth ionsdispersed therein, and the nuclear spin of each rare earth ion formssuperposed states. The rare-earth dispersed crystal 404 is a solidmaterial succeeded in realization of electromagnetically inducedtransparency (EIT). The material that has realized EIT can hold quantummechanically superposed states for an especially long time for a solid,and the quantum states can be operated and observed using light. EIT isa phenomenon that drastically changes the optical properties. EIT causessuperposed states in which no light absorption is performed, and noatoms or ions are excited into a higher energy state. The material thatrealizes solid EIT is, for example, crystal (Pr³⁺:Y₂SiO₅) containingrare-earth ions, and a level system including the hyperfine structurelevels of the ions is used.

The rare-earth dispersed crystal 404 is oxide crystal containing rareearth ions. The first embodiment employs crystal of Pr³⁺:Y₂SiO₅ in which0.01% y³⁺ ions are replaced with Pr³⁺ ions. The physical systemsrepresenting quantum bits are Pr³⁺ ions contained in Pr³⁺:Y₂SiO₅crystal. The rare-earth dispersed crystal 404 has a size of about 1 mm×1mm×1 mm, and a mirror of an ultrahigh reflectance is formed on itssurface, thereby providing a resonator structure.

The resonator 405 has a resonator mode. The resonator mode is made toresonate with the transition between ³H₄ and ¹D₂ concerning Pr³⁺ ions.

The coils 406 to 408 are provided around the crystal, as shown in FIG.4, for applying a magnetic field of a preset direction and intensity tothe crystal. In FIG. 4, the coils 406 and 407 are arranged around therare-earth dispersed crystal 404, and a pair of coils 408 are arrangedwith a certain plane interposed between a pair of coils 408, the certainplane including the centers of the coils 406 and 407.

The cryostat 409 maintains its internal temperature at 1.5 K.

Referring to FIG. 5, a description will now be given of the suppressionof de-coherence between two energy states that occurs when a magneticfield is applied to the rare-earth dispersed crystal 404. FIG. 5 showsthe energy states of three Pr³⁺ ions utilized in the first embodimentwhen a magnetic field is applied.

In the case of FIG. 5, the coils 406 to 408 apply a magnetic field tothe rare-earth dispersed crystal 404 so that two energy states of acertain ion, i.e., |±½> and |± 3/2> (=electronic ground states ³H₄),will be set to the critical point. Specifically, the coils 406, 407 and408 apply magnetic fields of 173 G, −219 G and 732 G to the C₂-axisdirection of the crystal, the polarization direction of the opticaltransition between ³H₄ and ¹D₂, and a direction perpendicular to thesetwo directions (i.e., the C₂-axis direction and the polarizationdirection), respectively. The direction and intensity of each magneticfield are unique to the transition energy between the corresponding twoenergy states representing quantum bits, and offset the lineartransition energy shift.

As shown in FIG. 5, the states generated by hyperfine structuresplitting from electronic ground state ³H₄ and electronic excited state¹D₂ are further split by the application of a magnetic field. The statesused in the first embodiment are |A′>, |A>, |B′>, |B>, |C′>, |C>, |D′>,|D>, |E′>, |E>, |F′> and |F> in the increasing order of energy. Thefirst embodiment utilizes three ions, in each of which all transitionsbetween |A> and |D> resonates in the common resonator mode.

Firstly, |A′>, |A>, |B′>, |B>, |C′>, |C>, |D′>, |D>, |E′>, |E>, |F′> and|F> will now be referred to as |2′>, |2>, |0′>, |0>, |1′>, |1>, |3′>,|3>, |4′>, |4>, |5′> and |5>, respectively. As shown, the transitionenergy between any two of the 12 energy states varies in a certainenergy range, except for between any two of the four energy states |2′>,|2>, |3′> and |3>. In this case, ions having different transitionfrequencies are utilized, and resonant ions can be selected by adjustingthe frequency of the light applied.

A description will be given of a gate operation performed on the statesof coherence acquired in the above. For the gate operation, it isnecessary to emit light to the rare-earth dispersed crystal 404.Referring to FIG. 6, the quantum information processing device of thefirst embodiment, which incorporates a unit used for the gate operation,will be firstly described.

The quantum information processing device of FIG. 6 comprises, as wellas the elements of the device shown in FIG. 4, a ring dye laser 601,four beam splitters 602, mirror 603, phase modulating EO modulators(EOMs) 604, intensity-modulating AO modulators (AOMs) 605,frequency-modulating AOMs 606, five mirrors 607, controller 608 andphotodetector 610. The controller 608 includes a magnetic-fielddesignation unit 612 and phase/intensity/frequency adjusting unit 609.In the following description, elements similar to the above-describedones will be denoted by the corresponding reference numbers, andduplication of explanation will be avoided. In FIG. 6, only two pairs ofcoils are provided, and the rotation-designating unit 403 is notemployed. Alternatively, the quantum information processing device ofFIG. 6 may employ a pair of coils and the rotation-designating unit 403,or may employ only three pairs of coils.

The ring dye laser 601 serves as a light source unit for generatinglight. The ring dye laser 601 includes a feedback system for suppressingfrequency jitters, and generates a laser beam with a low frequency ofseveral kHz.

The beam splitter 602 receives light from the ring dye laser 601, andsplits the received light in transmission light and reflected light. Inthe example of FIG. 6, the four beam splitters 602 split the light fromthe ring dye laser 601 into five light beams. The mirror 603 receivesand reflects the light passing through the last one (i.e., the uppermostone in FIG. 6) of the beam splitters 602.

The phase modulating EOMs 604 receive the light beams from therespective beam splitters 602 and mirror 603, and modulate the phases ofthe light beams. The intensity-modulating AOMs 605 receive light beamsfrom the respective phase modulating EOMs 604, and modulate theintensity of the light beams. The frequency-modulating AOMs 606 receivethe light beams from the respective intensity-modulating AOMs 605, andmodulate the frequencies of the light beams.

The mirrors 607 reflect the light beams from the respectivefrequency-modulating AOMs 606. The mirrors 607 are adjusted to guide thelight beams to the rare-earth dispersed crystal 404.

The photodetector 610 incorporates a light converging system of a highefficiency, and detects, with high sensitivity and high efficiently, thephotons generated by ions in the rare-earth dispersed crystal 404 whenlight is applied to the crystal.

The controller 608 controls the current flowing through the coils 406and 407 for generating a magnetic field applied to the rare-earthdispersed crystal 404, and controls the phase modulating EOMs 604,intensity-modulating AOMs 605 and frequency-modulating AOMs 606. Thephase/intensity/frequency adjusting unit 609 determines the values towhich the respective phase modulating EOMs 604 modulate the phases ofthe light beams to thereby adjust the phase modulating EOMs 604,determines the values to which the intensity-modulating AOMs 605modulate the intensity of the respective light beams, and determines thevalues to which the frequency-modulating AOMs 606 modulates thefrequencies of the respective light beams.

Referring to FIG. 5, the gate operation will be described.

Firstly, five light beams are sequentially applied to ion 1, ion 2, andion 3, and each of five light beams simultaneously is applied the ion 1,ion 2, and ion 3, using the apparatus of FIG. 6, thereby initializingthe state of each of the ions to |0> or |1>. To initialize, for example,ion 1 to |0>, light beams that resonate with the transition between |2′>and |4′>, between |2> and |4>, between |0′> and |3′>, between |1> and|5′> and between |1> and |5> are simultaneously applied to therare-earth dispersed crystal 404. Thus, ions 1, 2 and 3 are firstlyinitialized to |0>.

Subsequently, adiabatic passage is performed between the transitionbetween |2>₃ and |4>₃ and the combination of the transition between |0>₃and |4>₃ and the transition between |1>₃ and |4>₃, using Gaussian pulselight with a pulse width of 10 μs that resonates with the transitionbetween |2>₃ and |4>₃, the transition between |0>₃ and |4>₃ and thetransition between |1>₃ and |4>₃ (firstly, Gaussian pulse light thatresonates with the transition between |2>₃ and |4>₃ is applied). Thesubscript of each energy state (i.e., k of |j>_(k) (j=0, 1, 2, 3, 4, 5;k=1, 2, 3)) is the number that indicates which one of ions 1, 2 and 3each energy state belongs to. The Gaussian pulse light with the pulsewidth of 10 μs is generated by the intensity-modulating AOMs 605.

Subsequently, adiabatic passage is performed between the combination oftwo transitions, i.e., the transition between |0>₃ and |3>₃ and thetransition between |1>₃ and |3>₃, and the combination of fourtransitions, i.e., the transition between |0>₁ and |3>₁, the transitionbetween |1>₁ and |3>₁, the transition between |0>₂ and |3>₂, and thetransition between |1>₃ and |3>₃, using Gaussian pulse light with apulse width of 10 μs that resonates with each of the transitions. Morespecifically, this adiabatic passage is performed by applying the lighttwice (i.e., by applying the light firstly to the former combination,and secondly to the latter combination, the phase of the secondlyapplied light being inverted).

Lastly, adiabatic passage inverse of the first case is performed betweenthe transition between |2>₃ and |4>₃ and the combination of thetransition between |0>₃ and |4>₃ and the transition between |1>₄ and|3>₄ (in this adiabatic passage, light is applied firstly to thecombination).

If the quantum bits are |0> and |1>, a series of gate operationsmentioned above is regarded as a quantum Toffoli gate operation forchanging the quantum states as follows:

(|0>₁, |0>₂, |0>₃)→(|0>₁, |0>₂, |0>₃)

(|0>₁, |1>₂, |0>₃)→(|0>₁, |1>₂, |0>₃)

(|1>₁, |0>₂, |0>₃)→(|1>₁, |0>₂, |0>₃)

(|1>₁, |1>₂, |0>₃)→(|1>₁, |1>₂, |1>₃)

If ions 1, 2 and 3 are initialized to (|0>₁, |0>₂, |0>₃), theabove-described quantum Toffoli gate operation is iterated three timesat intervals of 10 ms, and the final results are read by lightapplication and photon detection, (|0>₁, |0>₂, |0>₃) are acquired as thefinal results. Similarly, if ions 1, 2 and 3 are initialized to (|0>₁,|1>₂, |0>₃), (|1>₁, |0>₂, |0>₃), and (|1>₁, |1>₂, |0>₃), and the quantumToffoli gate operation is iterated three times for the respectiveinitialization cases, (|0>₁, |1>₂, |0>₃) (|1>₁, |0>₂, |0>₃) and (|1>₁,|1>₂, |1>₃) are acquired as the final results.

If the sequence consisting of three successive quantum Toffoli gateoperations is iterated a large number of times, and the final resultsare read, (|0>₁, |0>₂, |0>₃), (|0>₁, |1>₂, |0>₃), (|1>₁, |0>₂, |0>₃) and(|1>₁, |1>₂, |1>₃) are acquired with a probability of 90% or more as thefinal results corresponding to the four initial states (|0>₁, |0>₂,|0>₃), (|0>₁, |1>₂, |0>₃), (|1>₁, |0>₂, |0>₃) and (|1>₁, |1>₂, |0>₃).This means that the quantum Toffoli gate operation, which has theproperty that when this operation is iterated an odd number of times,the state of the target bit (the quantum bit indicated by ion 3) isreversed only if the two control bits (the quantum bits indicated byions 1 and 2) assume states of (1, 1), is correctly executed with a highprobability for a long gate operation time of about 30 ms. 10 ms is setassuming information processing using a large number of quantum bits,and is set as a time for which quantum bits other than theabove-mentioned ones are operated, or as a time for which each quantumToffoli gate operation is performed while quantum bits are representedusing only |0>and |1>.

A description will be given of the case where the quantum Toffoli gateoperation cannot correctly be executed if one of the two energy statesset to the critical point is one of the two energy states (|C>, |D>)that resonate in the resonator mode.

When a magnetic field is applied, three ions 4, 5 and 6, in which allthe transitions between |C>and |D>resonate in the resonator mode, areselected. Concerning these three ions, |A′>, |A>, |B′>, |B>, |C′>, |C>,|D′>, |D>, |E′>, |E>, |F′>and |F> will now be referred to as |0′>, |0>,|1′>, |1>, |2′>, |2>, |3′>, |3>, |4′>, |4>, |5′> and |5>, respectively.Also in ions 4, 5 and 6, the transition energy between any two of the 12energy states varies in a certain energy range, except for between anytwo of the energy states |2′>, |2>, |3′> and |3>. In this case, ionshaving different transition frequencies are utilized, and resonant ionscan be selected by adjusting the frequency of the light applied.

In the same manner as in the case of ions 1, 2 and 3, ions 4, 5 and 6are set to initial states (|1>₄, |1>₅, |0>₆). Further, in the samemanner as in the case of ions 1, 2 and 3, the sequence, which consistsof three successive quantum Toffoli gate operations performed atintervals of 10 ms and reading of final results by light application andphoton detection, is iterated a large number of times. In this case,(|1>₄, |1>₅, |1>₆) and (|1>₄, |1>₅, |0>₆) irregularly appear as thefinal results. This means that concerning ions 4, 5 and 6, the quantumToffoli gate operation is not correctly performed.

In the case of ions 1, 2 and 3, the two energy states set to thecritical point when a magnetic field is applied thereto are energystates (|B>, |C>) that are included in the energy states (|A>, |B>, |C>)indicating quantum bits and do not include the two energy states (|A>,|D>) that resonate in the resonator mode. In contrast, in the case ofions 4, 5 and 6, one (|C>) of the two energy states (|B>, |C>) set tothe critical point when a magnetic field is applied thereto is includedin the two energy states (|C>, |D>) that resonate in the resonator mode.The quantum information processing method and device of the firstembodiment can confirm that when the two energy states, which areincluded in energy states indicating quantum bits and set to thecritical point when a magnetic field is applied thereto, do not includean energy state that resonates in the resonator mode, the coherence timeincreased by the application of the magnetic field works effectively,and a series of quantum gate operations is performed normally.

It can be confirmed from the quantum information processing method anddevice of the first embodiment that a pair of energy states included inthe energy states indicating quantum bits and not degenerated when nomagnetic field is applied can effectively utilize the coherence timeincreased when a magnetic field of a particular direction and intensityis applied to rare-earth-dispersed crystal, and can normally perform aseries of quantum gate operations.

Second Embodiment

Referring to FIG. 6, a quantum information processing method and deviceaccording to a second embodiment will be described.

The second embodiment is directed to the above-described case (2) wherethe coherence time between energy states that are degenerated when nomagnetic field is applied is extended by the application of a magneticfield.

The quantum information processing device of the second embodiment shownin FIG. 6 is similar to that of the first embodiment, except for thefollowing points:

In the second embodiment, the coils 406 and other coils are providedaround crystal in the same manner as in the first embodiment shown inFIG. 4. However, in the second embodiment, the coils 406 and other coilsapply a magnetic field of 30 G in a direction perpendicular to both theC₂-axis of the crystal and the polarization direction of the opticaltransition between ³H₄ and ¹D₂. Although in the second embodiment, thedirection of the magnetic field is designated, it is important in thesecond embodiment to apply a magnetic field, and the direction of themagnetic field is not so important as in the first embodiment.

The magnetic-field designation unit 402 can supply a current to thecoils 406 and other coils, or interrupt the supply of the current.

Also in the second embodiment, the energy states of Pr³⁺ ions releasedfrom the degenerated states by the applied magnetic field are utilizedas in the case of FIG. 5. The second embodiment utilizes two ions inwhich all transitions between |B> and |D> (|B′> and |D′>) resonate in acommon resonator mode when no magnetic field is applied.

In the second embodiment, |A′>, |A>, |B′>, |B>, |C′>, |C>, |D′>, |D>,|E′>, |E>, |F′> and |F> will be referred to as |1>, |0>, |2>, |3>, |4>,|5>, |6>, |7>, |8>, |9>, |10> and ||11>, respectively. The transitionenergy between any two of the 12 energy states |0> to |11>of each ionvaries in a certain energy range, except for between any two of theenergy states |2>, |3>, |6> and |7>. In this case, ions having differenttransition frequencies are utilized, and resonant ions can be selectedby adjusting the frequency of the light applied.

Referring to FIG. 7, the gate operation performed in the secondembodiment will be described. FIG. 7 shows the energy states of two ions7 and 8 utilized in the second embodiment.

Five light beams are sequentially applied to ion 7 and ion 8, and eachof five light beams simultaneously is applied the ion 7 and ion 8,thereby initializing the states of the ions to |0>₇ and |1>₈,respectively. As the five light beams simultaneously applied to ions 7and 8, light beams that resonate with the transition between |1> and|6>, between |2> and |8>, between |3> and |9>, between |4> and |10> andbetween |5> and |11> are used.

Subsequently, adiabatic passage is performed on ions 7 and 8 threetimes, using two Gaussian pulse light beams with a pulse width of 10 μs,thereby realizing quantum state shifts of |0>₇→|2>₇, |0>₈→|2>₈ and|1>₈→|3>₈.

After that, the application of the magnetic field is interrupted, andadiabatic passage is performed on ions 7 and 8, using Gaussian pulselight with a pulse width of 10 ∥s that resonates with the transitionbetween |1> and |6> (|0> and |7>), thereby exchanging the quantum statesof ions 7 and 8 for each other.

Thereafter, the application of the same magnetic field as before isstarted, and the quantum state of ion 8 is exchanged between |1> and |0>by applying light, and adiabatic passage is again performed on ions 7and 8, using light that resonates with the transition between |1> and|6> (|0> and |7>), thereby exchanging the quantum states of ions 7 and 8for each other. Further, adiabatic passage is performed on ions 7 and 8three times, using two light beams, thereby returning the quantum bitsto the original energy states |0> and |1>.

If the quantum bits are |0> and |1>, a series of gate operationsmentioned above is regarded as a control NOT gate operation for changingthe quantum states as follows:

(|0>₇, |0>₈)→(|0>₇, |0>₈)

(|0>₇, |1>₈)→(|0>₇, |1>₈)

(|1>₇, |0>₈)→(|1>₇, |1>₈)

(|1>₇, |1>₈)→(|1>₇, |0>₈)

If ions 7 and 8 are initialized to (|0>₇, |0>₈), the above-describedcontrol NOT gate operation is iterated seven times, and the finalresults are read by light application and photon detection, (|0>₇, |0>₈)are acquired as the final results. Similarly, if ions 7 and 8 areinitialized to (|0>₇, |1>₈), (|1>₇, |0>₈) and (|1>₇, |1>₈), and theabove-described-7-times control NOT gate operation is iterated threetimes for the respective initialization cases, (|0>₇, |1>₈), (|1>₇,|1>₈) and (|1>₇, |0>₈) are acquired as the final results. If thesequence consisting of seven successive control NOT gate operations isiterated a large number of times, and the final results are read, (|0>₇,|0>₈), (|0>₇, |1>₈), (|1>₇, |1>₈) and (|1>₇, |0>₈) are acquired with aprobability of 90% or more as the final results corresponding to thefour initial states (|0>₇, |0>₈), (|0>₇, |1>₈), (|1>₇, |0>₈) and (|1>₇,|1>₈). This means that the control NOT gate operation, which has theproperty that when this operation is iterated an odd number of times,the state of the target bit (the quantum bit indicated by ion 8) isreversed only if the control bit (indicated by ion 7) assumes a state of|1>, is correctly executed with a high probability as large as seventimes for a long time of about 5 ms.

In the above-described quantum information processing devices andmethods of the embodiments, where energy states indicating quantum bitsare degenerated when no magnetic field is applied, if a magnetic fieldis always applied, and the application of the magnetic field isinterrupted only if two-qbit-gate adiabatic passage is performed, thecoherence time increased by the application of the magnetic field can beeffectively utilized, and a series of quantum gate operations can benormally performed.

The above-described embodiments can also extend the time of each gateoperation. Accordingly, in quantum information processing in whichquantum bits are discriminated from each other by their frequencyregions (i.e., their transition energy), the frequency (energy)resolution can be enhanced, with the result that the number of quantumbits can be increased.

In addition, the above-described embodiments can provide methods for usein a quantum information processing device that uses, as quantum bits,physical systems magnetically influencing each other, and uses aresonator mode. These methods can actually utilize, for quantuminformation processing, the coherence time of quantum bits significantlyincreased by the application of a magnetic field.

Additional advantages and modifications will readily occur to thoseskilled in the art. Therefore, the invention in its broader aspects isnot limited to the specific details and representative embodiments shownand described herein. Accordingly, various modifications may be madewithout departing from the spirit or scope of the general inventiveconcept as defined by the appended claims and their equivalents.

1. A quantum information processing device comprising: a resonatorincorporating a material containing a plurality of physical systems,each of the physical systems having at least four energy states,transition between two energy states of the at least four energy states,and transition energy between at least two energy states of the at leastfour energy states, the at least four energy states being non-degeneratewhen a magnetic field fails to be applied to the physical systems, thetransition resonating in resonator mode that is in common between thephysical systems, each of the at least four energy states representing aquantum bit, the transition energy being shifted when the magnetic fieldis applied to the physical systems; and a magnetic-field applicationunit configured to apply a magnetic field having a direction and anintensity to the material, to eliminate a linear transition energy shiftbetween two energy states included in the physical systems, each of thetwo energy states included in the physical systems being with excludingthe two energy states resonating in the resonator mode.
 2. The deviceaccording to claim 1, wherein each of the physical systems includes arare earth ion contained in oxide crystal.
 3. The device according toclaim 1, further comprising a cryostat which holds interior at aconstant temperature, and contains the resonator, the material and themagnetic-field application unit.
 4. The device according to claim 1,wherein the magnetic-field application unit includes at least two pairsof electromagnets.
 5. The device according to claim 1, wherein themagnetic-field application unit includes at least one pair ofelectromagnets and a rotary unit configured to rotate the material aboutthree axes which fail to be parallel to each other.
 6. A quantuminformation processing device comprising: a resonator incorporating amaterial containing a plurality of physical systems, each of thephysical systems having a plurality of energy states and transitionbetween two energy states of the plurality of energy states, thetransition resonating in the resonator mode that is in common betweenthe physical systems, each of energy states that are degenerate and areincluded in the plurality of energy states representing a quantum bit; amagnetic-field application unit configured to apply a magnetic field tothe physical systems; a light source unit configured to output a laserbeam; a separation unit configured to separate the laser beam into aplurality of laser beams; a laser control unit configured to controlphase, intensity and frequency of each of the laser beams, the lasercontrol unit converting the laser beams into pulse laser beams; anemission unit configured to emit the controlled laser beams to thephysical systems; and a magnetic-field control unit configured tocontrol application of the magnetic field, the magnetic-field controlunit causing the magnetic-field application unit to interrupt theapplication of the magnetic field only when adiabatic passage for atwo-qbit (i.e., quantum bit) gate operation is performed between two ofthe physical systems utilizing the resonator mode.
 7. The deviceaccording to claim 6, wherein each of the physical systems includes arare earth ion contained in oxide crystal.
 8. The device according toclaim 1, further comprising a cryostat which holds interior at aconstant temperature, and contains the resonator, the material and themagnetic-field application unit.
 9. The device according to claim 6,wherein the magnetic-field application unit includes at least two pairsof electromagnets.
 10. The device according to claim 6, wherein themagnetic-field application unit includes at least one pair ofelectromagnets and a rotary unit configured to rotate the material aboutthree axes which fail to be parallel to each other.
 11. A quantuminformation processing method comprising: preparing a resonatorincorporating a material containing a plurality of physical systems,each of the physical systems having at least four energy states,transition between two energy states of the at least energy states, andtransition energy between at least two energy states of the at leastfour energy states, the at least four energy states being non-degeneratewhen a magnetic field fails to be applied to the physical systems, thetransition resonating in resonator mode that is in common between thephysical systems, each of the at least energy states representing aquantum bit, the transition energy being shifted when the magnetic fieldis applied to the physical systems; and applying a magnetic field havinga direction and an intensity to the material, to eliminate a lineartransition energy shift between two energy states included in thephysical systems, each of the two energy states included in the physicalsystems being with excluding the two energy states resonating in theresonator mode.
 12. The method according to claim 11, wherein each ofthe physical systems includes a rare earth ion contained in oxidecrystal.
 13. The method according to claim 11, further comprisingpreparing a cryostat which holds interior at a constant temperature, andcontains the resonator and the material.
 14. A quantum informationprocessing method comprising: preparing a resonator incorporating amaterial containing a plurality of physical systems, each of thephysical systems having a plurality of energy states and transitionbetween two energy states of the plurality of energy states, thetransition resonating in the resonator mode that is in common betweenthe physical systems, each of energy states that are degenerate and areincluded in the plurality of energy states representing a quantum bit;applying a magnetic field to the physical systems; outputting a laserbeam; separating the laser beam into a plurality of laser beams;controlling phase, intensity and frequency of each of the laser beams,converting the laser beams into pulse laser beams; emitting thecontrolled laser beams to the physical systems; controlling applicationof the magnetic field; and interrupting the application of the magneticfield only when adiabatic passage for a two-qbit (i.e., quantum bit)gate operation is performed between two of the physical systemsutilizing the resonator mode.
 15. The method according to claim 14,wherein each of the physical systems includes a rare earth ion containedin oxide crystal.
 16. The method according to claim 14, furthercomprising preparing a cryostat which holds interior at a constanttemperature, and contains the resonator and the material.